Among the people I interact with in the geodynamics community, it seems that almost all of us are in full support of the mantle plume theory. What are the strongest arguments against this theory? Is the earth science community not as divided on this subject as some people have led me to believe ?
The best argument I've heard supporting strong skepticism of plumes, if not total dismissal, is that the theory is too flexible. To put it more bluntly, this amounts to saying that it is unfalsifiable and therefore not helpful (in Popper's words, "A theory that explains everything, explains nothing.").
Erik Lundin, a Norwegian geologist, is a fairly vociferous (and sarcastic) proponent of this view. He likes to point out that you can explain almost any tectonic anomaly with plumes. Have a look at his articles The Iceland “Anomaly” – An Outcome of Plate Tectonics and Phanerozoic fold belts and volcanic passive margins: a causal relationship? on Gillian Foulger's site mantleplumes.org — where you'll find lots of other evidence for and against plumes.
My own view is that there seems to be some clear cases of plume-like things being a good explanation for observations — the Hawaiian–Emperor chain comes to mind. And then there's the rest of the infinitely complex earth, with thousands of competing and interacting forces, convection currents being just one.
As mentioned, the theory is so vague that it's impossible to falsify nor support it with present methods and data. Geologists can learn something about the limitation of tomographic models in this overview: Foulger et al 2013. Even the mantle plume model for the Emperor Chain have been challenged in some studies. One of the strongest arguments comes from Cande et al 1995, who shows that the tectonic movements and the locations of the sea-mount chain don't agree. (However, the study has itself been questioned.)
The only strong supportive argument from seismic data I could think of would be if guided waves were detected as suggested by Julian and Evans 2010, but as far as I know (please correct me!) there is yet no study that have seen it.
I can't be sure that plumes don't exist, but I'm afraid that the simplified theory obscures more complex and true models about mantle dynamics.